Nilpotency and spectral operators

Maps preserving the nilpotency of products of operators

Let B(X) be the algebra of all bounded linear operators on the Banach space X, and let N (X) be the set of nilpotent operators in B(X). Suppose φ : B(X)→ B(X) is a surjective map such that A,B ∈ B(X) satisfy AB ∈ N (X) if and only if φ(A)φ(B) ∈ N (X). If X is infinite dimensional, then there exists a map f : B(X)→ C \ {0} such that one of the following holds: (a) There is a bijective bounded li...

Hill Operators and Spectral Operators of Scalar

We derive necessary and sufficient conditions for a one-dimensional periodic Schrödinger (i.e., Hill) operator H = −d 2 /dx 2 + V in L 2 (R) to be a spectral operator of scalar type. The conditions demonstrate the remarkable fact that the property of a Hill operator being a spectral operator is independent of smoothness (or even analyticity) properties of the potential V. R ´ ESUMÉ. Quand un op...

wavelets, modulation spaces and pseudidifferential operators

مبحث تحلیل زمان-فرکانسی سیگنالها یکی از مهمترین زمینه های مورد بررسی پژوهشگران علوم ÷ایه کاربردی و فنی مهندسی میباشد.در این پایان نامه فضاهای مدولاسیون به عنوان زمینه اصلی این بررسی ها معرفی گردیده اند و نتایج جدیدی که در حوزه های مختلف ریاضی،فیزیک و مهندسی کاربرداساسی و فراوانی دارند استوار و بیان شده اند.به ویژه در این پایان نامه به بررسی و یافتن مقادیر ویژه عملگر های شبه دیفرانسیل با سمبل در...

Block Operators and Spectral Discretizations

Every student of numerical linear algebra is familiar with block matrices and vectors. The same ideas can be applied to the continuous analogues of operators, functions, and functionals. It is shown here how the explicit consideration of block structures at the continuous level can be a useful tool. In particular, block operator diagrams lead to templates for spectral discretization of differen...

Dirac Operators and Spectral Geometry